How Does Force Affect Velocity in a One-Dimensional System?

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The discussion focuses on calculating the velocity of a 1.8 kg body influenced by a force defined as Fx = -6x N as it moves along the positive x-axis. To find the velocity at x = 4.0 m, participants suggest integrating the force function to determine the work done. The confusion arises regarding the relationship between force, work, and velocity, with clarification that the integral of the force function represents the total work. Participants emphasize that the work done is not simply the product of force and displacement. The conversation highlights the importance of understanding the integral in the context of force and motion.
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The only force acting on a 1.8 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.



(a) What is the velocity of the body at x = 4.0 m?

(b) At what positive value of x will the body have a velocity of 5.0 m/s?



I think to start off i need to take the integral of Fx=-6xN, which would be -3x^2. But from there I'm a bit confused. It doesn't give the force acting on it, so i don't know how to find the work since W=F*Fx.
 
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brittkub1291 said:
The only force acting on a 1.8 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.
(a) What is the velocity of the body at x = 4.0 m?

(b) At what positive value of x will the body have a velocity of 5.0 m/s?
I think to start off i need to take the integral of Fx=-6xN, which would be -3x^2. But from there I'm a bit confused. It doesn't give the force acting on it, so i don't know how to find the work since W=F*Fx.
The integral you did IS the work.
You did integral of Fx*dx and this is dW . The integral is the total work.

And no, the work is not W=F*Fx.
Fx is the force
 

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